Question

State the law of conservation of linear momentum

Answer 1

First off momentum = mass x velocity. You can prove the conservation of momentum (i.e. that it stays the same unless a force acts upon a body) from Newton's laws.

Force = mass x acceleration

Acceleration is the change of velocity over time so:

Force = mass x ((velocity1 - velocity2) / time)

Or:

Force = ((mass x velocity1) - (mass x velocity2)) / time

Because mass x velocity is momentum, we can say:

Force = (momentum1 - momentum2) / time

Or:

Force x time = momentum1 - momentum2

Meaning a change in momentum is caused by force multiplied by time. If there is no force (or no time for it to be applied), the left hand side of the equation is zero, meaning momentum1 = momentum2 (and therefore there is no change in momentum).

Therefore, without a force being applied for a period of time, momentum is conserved.

Answer 2

The law of conservation of linear momentum states that if no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their mutual interaction.